Lie symmetries of Generalized Equal Width wave equations

• Published in: AIMS mathematics Vol. 6; no. 11; pp. 12148 - 12165
• Main Authors: Munir, Mobeen, Athar, Muhammad, Sarwar, Sakhi, Shatanawi, Wasfi
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2021
• Subjects: generalized equal width wave equation; lie symmetry; optimal system; reduction; sine-cosine method; travelling wave solution
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021705

Lie symmetry analysis of differential equations proves to be a powerful tool to solve or atleast to reduce the order and non-linearity of the equation. The present article focuses on the solution of Generalized Equal Width wave (GEW) equation using Lie group theory. Over the years, different solution methods have been tried for GEW but Lie symmetry analysis has not been done yet. At first, we obtain the infinitesimal generators, commutation table and adjoint table of Generalized Equal Width wave (GEW) equation. After this, we find the one dimensional optimal system. Then we reduce GEW equation into non-linear ordinary differential equation (ODE) by using the Lie symmetry method. This transformed equation can take us to the solution of GEW equation by different methods. After this, we get the travelling wave solution of GEW equation by using the Sine-cosine method. We also give graphs of some solutions of this equation.